Improved Perturbation Theory and Four-Dimensional Space-Time in IIB Matrix Model

TL;DR

This paper applies an improved mean field approximation to the IIB matrix model, providing evidence that a four-dimensional space-time emerges as the most stable vacuum configuration.

Contribution

The authors reformulate the improved mean field approximation and demonstrate its effectiveness in analyzing the IIB matrix model at higher orders.

Findings

Improved free energy shows a plateau indicating convergence.

Four-dimensional space-time appears as the most stable vacuum.

IMFA is validated as a systematic method for this model.

Abstract

We have analyzed IIB matrix model based on the improved mean field approximation (IMFA) and have obtained a clue that the four-dimensional space-time appears as its most stable vacuum. This method is a systematic way to give an improved perturbation series and was first applied to IIB matrix model by Nishimura and Sugino. In our previous paper we reformed this method and proposed a criterion for convergence of the improved series, that is, the appearance of the ``plateau''. In this paper, we perform higher order calculations, and find that our improved free energy tends to have a plateau, which shows that IMFA works well in IIB matrix model.